Nonsymmetric algebraic Riccati equations associated with an M-matrix: recent advances and algorithms

Authors Dario A. Bini, Bruno Iannazzo, Beatrice Meini, Federico Poloni



PDF
Thumbnail PDF

File

DagSemProc.07461.11.pdf
  • Filesize: 331 kB
  • 31 pages

Document Identifiers

Author Details

Dario A. Bini
Bruno Iannazzo
Beatrice Meini
Federico Poloni

Cite AsGet BibTex

Dario A. Bini, Bruno Iannazzo, Beatrice Meini, and Federico Poloni. Nonsymmetric algebraic Riccati equations associated with an M-matrix: recent advances and algorithms. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, pp. 1-31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
https://doi.org/10.4230/DagSemProc.07461.11

Abstract

We survey on theoretical properties and algorithms concerning the problem of solving a nonsymmetric algebraic Riccati equation, and we report on some known methods and new algorithmic advances. In particular, some results on the number of positive solutions are proved and a careful convergence analysis of Newton's iteration is carried out in the cases of interest where some singularity conditions are encountered. From this analysis we determine initial approximations which still guarantee the quadratic convergence.
Keywords
  • Nonsymmetric algebraic Riccati equations
  • matrix equation
  • M-matrices
  • Newton method
  • quadratically convergent algorithms
  • cyclic reduction
  • doubling

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail